For Teamleader specifically, the price hinges on that invoicing decision more than on the API work itself: a CRM-and-quotes-only connection is at the lower end of the range, while one that also has to reconcile Teamleader against a separate accounting package is closer to two projects than one.
A connection starts from €1,700 plus a monthly service fee, which covers the monitoring, the queue and keeping up with the vendor's API changes. Work outside a fixed scope is €95 per hour.
What moves the number is not the tool — it is how well the system on the other end is known. If JKC built your website, your webshop or your web application, we already know its data model, its edge cases and where its stock numbers really come from, and a connection into it is mostly configuration and testing. If it is a system we have never opened, we start with a short technical check of both sides and quote after that, so you are not paying hourly for us to work out the basics.
Two more things that move it, in our experience more than anything else: whether the tool has a real API or only a CSV export, and whether the sync has to go both ways. One-way is roughly half the work of two-way, because two-way means deciding, per field, which system wins when they disagree — and that decision is the expensive part, not the code.